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Journal of Atomic and Molecular Physics

Elastic Scattering of Sodium Atoms at Ultracold Temperatures

Jicai Zhang, Jinfeng Sun, Jiemin Wang

Published Feb 20, 2007• 0 citations
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Abstract

The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.

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The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.
Based on the accurate singlet and triplet state interatomic potentials for Na2, a theoretical study of elastic scattering properties of sodium atoms at ultracold temperatures is reported in this paper. The s-wave scattering length, effective range, the p-wave scattering length and the number of bound states are calculated. The singlet and triplet elastic scattering cross section between sodium aotms at ultracold temperatures are dominated by s-wave scattering, and shape resonances occur with collision energy increasing. There exist pronounced f-wave and i-wave shape resonances for the singlet and triplet cross section. In addition, s-wave scattering length is calculated by using the degenerate internet state approximation for selected hyperfine states of sodium atoms. The results are in agreement with calculated values obtained by close-coupling method.
The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7 a 0 for the singlet state and 33.4 a 0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.
The elastic scattering properties for collisions between cold and ultracold 39 K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet a 3 ∑ u + ground state of K 2 . Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578 a 0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the a 3 ∑ u + state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the a 3 ∑ u + state are calculated.
We report the calculation of the same-species elastic scattering properties for the ultracold rubidium–rubidium ( 85 Rb– 85 Rb) system and the results are compared with other theoretical and experimental results in detail. We present an improved potential for triplet ground states of the Rb 2 molecule, and calculate the scattering lengths a t and the effective range r e using WKB and Numerov methods for two rubidium-85 collisions in the triplet state. Also, we investigate the convergence of these scattering properties, i.e. the dependence on core radius and K 0 parameter using quantum defect theory and the analytic calculations of scattering length obtained by Szmytkowski. In addition, we present evaporative cooling and other results that include phase shift and cross section at zero energy limit.
The elastic scattering properties between ultracold 23 Na and 85 Rb atoms for the triplet state (a 3 Σ + u ) are researched. The s-wave scattering lengths of 23 Na and 85 Rb are calculated by the Numerov and semiclassical method with two kinds of interatomic potentials, which are the interpolation potential and Lennard—Jones potential (LJ 12,6 ) by the same phase Φ. Shape resonances appear clearly in the l = 5 partial waves for the a 3 Σ + u state. Moreover, the s-wave scattering cross section, total cross section and energy positions of shape resonances are also discussed.
The elastic scattering properties for collisions between ultracold Na and K atoms in the singlet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for the singlet X 1 Σ g + ground state of NaK. By means of the Numerov and semiclassical methods, the values of the s-wave scattering length a for the singlet state are calculated to be 33.3757 a 0 and 37.9399 a 0 , respectively. Pronounced shape resonances appear for the l = 1 partial wave for the X 1 Σ g + state. In addition, the s-wave scattering cross section, total cross section and energy positions of shape resonances for the X 1 Σ g + state are discussed.